cnc tube notcher

What you describe is a friction drive which I considered. There are
pipe welders with this configuration. But there are issues with
friction drive as well.

As for standard formulas for pipe intersections there are no
formulas (to my knowledge) but there are templates that you can
construct with old fasioned drafting techniques. But these templates
are extremely limited. The machine I designed allows you to intersect a
round tube with any shape (rectangle, planes, etc) and allows multiple
tube intersections like an exhaust manifold. It also maintains the
angular relationship between joints on either end of the tube, which is
the hardest part to "eyball" when building chassis via the traditional
methods of closed loop "grind and check".
The problem with notching tube this way is that the wall thickness
messes up the theoretical "perfect" joint and has to be corrected
for. Any joint cut at any angle other than 90 degrees has this
problem, and it can get very tricky to deal with. This is why race car
chassis and such (tubular space frames) are still built by hand.
Joint Jiggers, and Hole Saw type tubing notchers cut "real" joints
but are severely limited when it comes to steep angles and multiple
intersections.
Peace.